Six degrees of Hungarian mathematician Paul Erdos?

Paul Erdos in 1992.Kmhkmh

Tuesday marks 20 years since the death of Hungarian mathematician Paul Erdos (1913-1996), an obsessive hunter of interesting problems and mathematical loose ends who, across a 70-plus-year career, published more than 1,500 papers. His habit of collaboration — working with no fewer than 511 coauthors — inspired the creation of Erdos numbers. Those 511 coauthors each have an Erdos number of 1; someone who wrote a paper with one of the 511 would have an Erdos number of 2; and so forth, each degree of separation increasing the number by one.

It’s an informal measure of a researcher’s connectedness, a source of playful bragging rights — or not so playful: One mathematician controversially attempted to auction a chance to piggyback on his comparatively low Erdos number. But, mathematicians being mathematicians, the numbers have themselves become a source of study, a way to investigate patterns of collaboration and the dissemination of ideas within and across fields. Thanks to interdisciplinary inquiry and the rise of computational analysis, Erdos numbers have reached far beyond mathematics. (Linguist Noam Chomsky has an Erdos number of 4; German Chancellor Angela Merkel, a former chemist, has an Erdos number of 5.)

It is, of course, similar to the pop-culture exercise of finding movie-cast chains of collaboration that end with actor Kevin Bacon. Musicians have another version of the game, centered around members of the heavy-metal band Black Sabbath. Like the Erdos number, the Bacon and Sabbath games play on the unexpected collapse of distance between seemingly far-flung points. (This writer, for instance, while bereft of an Erdos number, can claim a Sabbath number of 5.)

But the parallels between music and mathematics raise an interesting puzzle: Which professional musician has the lowest Erdos number? There is no shortage of musicians that can make the connection. Jazz pianist Vijay Iyer, for example, thanks to an interest in computational models of music, has an Erdos number of 6; Brian May, guitarist for the band Queen, with a PhD in astrophysics, rates a 5; papers on probability and statistics garnered longtime mathematician and sometime satirical singer-songwriter Tom Lehrer a 4. Lower than that? One finds Glenn Turner, mathematics professor and founding guitarist of the seminal punk band the Angry Samoans (Erdos number 3), alongside classical pianists (and professors) Eugenia Cheng and Per Enflo (Erdos number 2). Even musically, it seems, Erdos numbers manage to exemplify their namesake’s broad, inexhaustible curiosity.

Matthew Guerrieri